Production and inventory management under multiple resource constraints

In this paper we present a model and solution methodology for production and inventory management problems that involve multiple resource constraints. The model formulation is quite general, allowing organizations to handle a variety of multi-item decisions such as determining order quantities, production batch sizes, number of production runs, or cycle times. Resource constraints become necessary to handle interaction among the multiple items. Common types of resource constraints include limits on raw materials, machine capacity, workforce capacity, inventory investment, storage space, or the total number of orders placed. For example, in a production environment, there may be limited workforce capacity and limits on machine capacities for manufacturing various product families. In a purchasing environment where a firm has multiple suppliers, there are often constraints for each supplier, such as the total order from each supplier cannot exceed the volume of the truck. We present efficient algorithms for solving both continuous and integer variable versions of the resource constrained production and inventory management model. The algorithms require the solution of a series of two types of subproblems: one is a nonlinear knapsack problem and the other is a nonlinear problem where the only constraints are lower and upper bounds on the variables. Computational testing of the algorithms is reported and indicates that they are effective for solving large-scale problems.